Spectral statistics of Bernoulli matrix ensembles-a random walk approach (I)

We investigate the eigenvalue statistics of random Bernoulli matrices, where the matrix elements are chosen independently from a binary set with equal probability. This is achieved by initiating a discrete random walk process over the space of matrices and analysing the induced random motion of the...

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Bibliographic Details
Published in:Journal of physics. A, Mathematical and theoretical Mathematical and theoretical, 2015-06, Vol.48 (25), p.255101-30
Main Authors: Joyner, Christopher H, Smilansky, Uzy
Format: Article
Language:English
Subjects:
complex systems
Gaussian
Mathematical analysis
Mathematical models
Matrices (mathematics)
Matrix methods
random graphs
random matrix theory
Random walk
Spectra
Statistics
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Summary:We investigate the eigenvalue statistics of random Bernoulli matrices, where the matrix elements are chosen independently from a binary set with equal probability. This is achieved by initiating a discrete random walk process over the space of matrices and analysing the induced random motion of the eigenvalues-an approach which is similar to Dyson's Brownian motion model but with important modifications. In particular, we show our process is described by a Fokker-Planck equation, up to an error margin which vanishes in the limit of large matrix dimension. The stationary solution of which corresponds to the joint probability density function of certain well-known fixed trace Gaussian ensembles.
ISSN:1751-8113
1751-8121
DOI:10.1088/1751-8113/48/25/255101